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\hypersetup{
  pdftitle={A hypothetical study using fake data to map K10 psychological distress and SOFAS functioning measures toAQoL-6D health utility using data from a sample of young people presenting to primary mental health services},
  pdfauthor={Alejandra R Scienceace1,2,; Fionn S Researchchamp3,2},
  pdfkeywords={anxiety, AQoL, CHU9D, psychological distress, QALYs, utility mapping},
  hidelinks,
  pdfcreator={LaTeX via pandoc}}

\title{A hypothetical study using fake data to map K10 psychological distress and SOFAS functioning measures toAQoL-6D health utility using data from a sample of young people presenting to primary mental health services}
\author{Alejandra R Scienceace\textsuperscript{1,2,*} \and Fionn S Researchchamp\textsuperscript{3,2}}
\date{}

\begin{document}
\maketitle
\begin{abstract}
\textbf{Background: } Quality Adjusted Life Years (QALYs) are often used in economic evaluations, yet utility weights for deriving them are rarely directly measured in mental health services. \newline \newline \textbf{Objectives: } We aimed to identify the best regression models to predict Adolescent AQoL Six Dimension (AQoL-6D) utility and evaluate the predictive ability of two candidate measures of psychological distress and functioning. \newline \newline \textbf{Methods: } The study sample is fake data.Five ordinary least squares (OLS) and three generalised linear models (GLMs) were explored to identify the best algorithm. Predictive ability of two candidate measures of psychological distress and functioning were assessed using ten fold cross validation and forest models. \newline \newline \textbf{Results: } K10 had the highest predictive ability in ten fold cross validation. GLM with Gaussian distribution and log link and OLS with complementary log log transformation were the best peforming models. \newline \newline \textbf{Conclusions: } Nothing should be concluded from this study as it is purely hypothetical. \newline \newline \textbf{Data: } Detailed results in the form of catalogues of the models produced by this study and other supporting information are available in the online repository: \url{https://doi.org/10.7910/DVN/LYBMB0} \newline \newline
\end{abstract}

\textsuperscript{1} Awesome University, Shanghai\\
\textsuperscript{2} August Institution, London\\
\textsuperscript{3} Highly Ranked Uni, Montreal

\textsuperscript{*} Correspondence: \href{mailto:fake_email@fake_institute.com}{Alejandra R Scienceace \textless{}\href{mailto:fake_email@fake}{\nolinkurl{fake\_email@fake}}\_institute.com\textgreater{}}

\hypertarget{introduction}{%
\section{Introduction}\label{introduction}}

This article is a scientific summary of a study that the authors implemented that has been automatically generated from study results by version 0.9.0.1 of the manuscript authoring program ttu\_lng\_ss {[}1{]}.

Quality Adjusted Life Years (QALYs) are often used in economic evaluations, yet utility weights for deriving them are rarely directly measured in mental health services.

The objective of the study was to identify the best utility mapping models to predict Adolescent AQoL Six Dimension (AQoL-6D) utility and evaluate the predictive ability of two candidate measures of psychological distress and functioning.

\hypertarget{methods}{%
\section{Methods}\label{methods}}

\hypertarget{sample-and-setting}{%
\subsection{Sample and setting}\label{sample-and-setting}}

The study sample is fake data.

\hypertarget{measures}{%
\subsection{Measures}\label{measures}}

Data was collected on utility weights, two candidate predictors of utility weights and descriptive population characteristics.

\hypertarget{utility-weights}{%
\subsubsection{Utility weights}\label{utility-weights}}

Utility weights were assessed using the AQoL-6D multi-attribute utility instrument.

\hypertarget{candidate-predictors}{%
\subsubsection{Candidate predictors}\label{candidate-predictors}}

Two measures of psychological distress (one measure) and functioning (one measure) were used as candidate predictors to construct models.

Psychological distress was measured by Kessler Psychological Distress Scale (10 Item) (K10 - measured on a scale of 10-50). Functioning was measured by Social and Occupational Functioning Assessment Scale (SOFAS - measured on a scale of 0-100).

\hypertarget{population-characteristics}{%
\subsubsection{Population characteristics}\label{population-characteristics}}

Population characteristic data were age, gender, aboriginal and torres strait islander, culturally and linguistically diverse, employment type, in education, education and employment, days unable to perform usual activities, days cut back on usual activities, days out of role, primary diagnosis group, area index of relative social disadvantage and area remoteness.

\hypertarget{statistical-analysis}{%
\subsection{Statistical analysis}\label{statistical-analysis}}

We implemented the generalised form of the study analysis algorithm developed by Hamilton, Gao and colleagues {[}2{]}, the key steps of which are summarised as follows.

\hypertarget{descriptive-statistics}{%
\subsubsection{Descriptive statistics}\label{descriptive-statistics}}

Basic descriptive statistics were used to characterise the cohort in terms of baseline population variables. Pearson's Product Moment Correlations (\emph{r}) were used to determine the relationships between candidate predictors and the AQoL-6D utility score.

\hypertarget{model-evaluation}{%
\subsubsection{Model evaluation}\label{model-evaluation}}

We compared predictive performance of a range of models predicting AQoL-6D utility scores using the candidate predictor that had the highest Pearson correlation coefficient with utility scores. The models compared include ordinary least squares (OLS) regression models and generalised linear models (GLMs). OLS regression models used no transformation, complementary log log transformation, log transformation, logit transformation and log log transformation. GLMs used gaussian distribution and log link, beta distribution and complementary log log link and beta distribution and logit link. Ten-fold cross-validation was used to compare model fitting with training datasets and predictive ability with testing datasets using three indicators including R\textsuperscript{2}, root mean square error (RMSE) and mean absolute error (MAE) {[}3,4{]}.

To evaluate whether candidate predictors could independently predict utility scores, we established multivariate prediction models using baseline data with the candidate predictor and demographic, clinical symptom and spatial covariates. Demographic covariates were aboriginal and torres strait islander, age, culturally and linguistically diverse, education and employment and gender. Clinical symptom covariates were days out of role and primary diagnosis group. Spatial covariates were area index of relative social disadvantage and area remoteness.

\hypertarget{candidate-predictor-comparison}{%
\subsubsection{Candidate predictor comparison}\label{candidate-predictor-comparison}}

We evaluated the independent predictive ability of different candidate predictors using 10-fold cross-validation.

\hypertarget{utility-mapping-models}{%
\subsubsection{Utility mapping models}\label{utility-mapping-models}}

We next established models using linear mixed effect models (LMMs) and generalised linear mixed effect models (GLMMs) . Model fitting was evaluated using Bayesian R\textsuperscript{2} {[}5{]}.

\hypertarget{software}{%
\subsubsection{Software}\label{software}}

We undertook all our analyses using R version 4.3.0 {[}6{]} using the TTU package {[}7{]} (version 0.0.0.9362).

\hypertarget{results}{%
\section{Results}\label{results}}

\hypertarget{cohort-characteristics}{%
\subsection{Cohort characteristics}\label{cohort-characteristics}}

Participants characteristics are displayed in Table \ref{tab:participantstb}. This study included all 3998 participants with complete AQoL-6D data.

\begin{table}

\caption{\label{tab:participantstb}Participant characteristics}
\centering
\begin{tabular}[t]{>{\raggedright\arraybackslash}p{14em}l>{\raggedright\arraybackslash}p{3em}>{\raggedright\arraybackslash}p{3em}}
\toprule
\multicolumn{1}{c}{ } & \multicolumn{1}{c}{ } & \multicolumn{1}{c}{ } & \multicolumn{1}{c}{ } \\

 &  & (N = & 3998)\\
\midrule
 & Mean (SD) & 17.692 & (3.477)\\
\cmidrule{2-4}
 & Median (Q1\, Q3) & 17.000 & (15.000\, 20.000)\\
\cmidrule{2-4}
 & Min - Max & 12.000 & 25.000\\
\cmidrule{2-4}
\multirow{-4}{14em}{\raggedright\arraybackslash \textbf{Age}} & Missing & 0.000 & \\
\cmidrule{1-4}
 & Female & 2457.000 & (61.456\%)\\
\cmidrule{2-4}
 & Male & 1451.000 & (36.293\%)\\
\cmidrule{2-4}
 & Other & 90.000 & (2.251\%)\\
\cmidrule{2-4}
\multirow{-4}{14em}{\raggedright\arraybackslash \textbf{Gender}} & Missing & 0.000 & \\
\cmidrule{1-4}
 & No & 3698.000 & (92.519\%)\\
\cmidrule{2-4}
 & Yes & 299.000 & (7.481\%)\\
\cmidrule{2-4}
\multirow{-3}{14em}{\raggedright\arraybackslash \textbf{Aboriginal and torres strait islander}} & Missing & 1.000 & \\
\cmidrule{1-4}
 & No & 2881.000 & (72.061\%)\\
\cmidrule{2-4}
 & Yes & 1117.000 & (27.939\%)\\
\cmidrule{2-4}
\multirow{-3}{14em}{\raggedright\arraybackslash \textbf{Culturally and linguistically diverse}} & Missing & 0.000 & \\
\cmidrule{1-4}
 & No & 2262.000 & (57.926\%)\\
\cmidrule{2-4}
 & Working casually & 940.000 & (24.072\%)\\
\cmidrule{2-4}
 & Working full-time & 309.000 & (7.913\%)\\
\cmidrule{2-4}
 & Working part-time & 394.000 & (10.090\%)\\
\cmidrule{2-4}
\multirow{-5}{14em}{\raggedright\arraybackslash \textbf{Employment type}} & Missing & 93.000 & \\
\cmidrule{1-4}
 & No & 1514.000 & (38.771\%)\\
\cmidrule{2-4}
 & Yes & 2391.000 & (61.229\%)\\
\cmidrule{2-4}
\multirow{-3}{14em}{\raggedright\arraybackslash \textbf{In education}} & Missing & 93.000 & \\
\cmidrule{1-4}
 & Not studying or working & 782.000 & (20.031\%)\\
\cmidrule{2-4}
 & Studying and working & 910.000 & (23.309\%)\\
\cmidrule{2-4}
 & Studying only & 1480.000 & (37.910\%)\\
\cmidrule{2-4}
 & Working only & 732.000 & (18.750\%)\\
\cmidrule{2-4}
\multirow{-5}{14em}{\raggedright\arraybackslash \textbf{Education and employment}} & Missing & 94.000 & \\
\cmidrule{1-4}
 & Mean (SD) & 9.827 & (8.854)\\
\cmidrule{2-4}
 & Median (Q1\, Q3) & 8.000 & (2.000\, 15.000)\\
\cmidrule{2-4}
 & Min - Max & 0.000 & 28.000\\
\cmidrule{2-4}
\multirow{-4}{14em}{\raggedright\arraybackslash \textbf{Days unable to perform usual activities}} & Missing & 1.000 & \\
\cmidrule{1-4}
 & Mean (SD) & 5.989 & (7.233)\\
\cmidrule{2-4}
 & Median (Q1\, Q3) & 3.000 & (0.000\, 10.000)\\
\cmidrule{2-4}
 & Min - Max & 0.000 & 28.000\\
\cmidrule{2-4}
\multirow{-4}{14em}{\raggedright\arraybackslash \textbf{Days cut back on usual activities}} & Missing & 3.000 & \\
\cmidrule{1-4}
 & Mean (SD) & 15.820 & (12.465)\\
\cmidrule{2-4}
 & Median (Q1\, Q3) & 15.000 & (4.000\, 26.000)\\
\cmidrule{2-4}
 & Min - Max & 0.000 & 56.000\\
\cmidrule{2-4}
\multirow{-4}{14em}{\raggedright\arraybackslash \textbf{Days out of role}} & Missing & 4.000 & \\
\cmidrule{1-4}
 & Anxiety and Depression & 952.000 & (28.866\%)\\
\cmidrule{2-4}
 & Not applicable & 2199.000 & (66.677\%)\\
\cmidrule{2-4}
 & Other Mental Disorder & 142.000 & (4.306\%)\\
\cmidrule{2-4}
 & Substance Use & 5.000 & (0.152\%)\\
\cmidrule{2-4}
\multirow{-5}{14em}{\raggedright\arraybackslash \textbf{Primary diagnosis group}} & Missing & 700.000 & \\
\cmidrule{1-4}
 & Mean (SD) & 5.288 & (2.774)\\
\cmidrule{2-4}
 & Median (Q1\, Q3) & 5.000 & (3.000\, 8.000)\\
\cmidrule{2-4}
 & Min - Max & 1.000 & 10.000\\
\cmidrule{2-4}
\multirow{-4}{14em}{\raggedright\arraybackslash \textbf{Area index of relative social disadvantage}} & Missing & 5.000 & \\
\cmidrule{1-4}
 & Inner Regional Australia & 1070.000 & (26.770\%)\\
\cmidrule{2-4}
 & Major Cities of Australia & 2441.000 & (61.071\%)\\
\cmidrule{2-4}
 & Outer Regional Australia & 438.000 & (10.958\%)\\
\cmidrule{2-4}
 & Remote/very remote Australia & 48.000 & (1.201\%)\\
\cmidrule{2-4}
\multirow{-5}{14em}{\raggedright\arraybackslash \textbf{Area remoteness}} & Missing & 1.000 & \\
\bottomrule
\end{tabular}
\end{table}

\hypertarget{aqol-6d-and-candidate-predictors}{%
\subsection{AQoL-6D and candidate predictors}\label{aqol-6d-and-candidate-predictors}}

Distribution of AQoL-6D total utility score and sub-domain scores are displayed in Figure \ref{fig:fig1}. The mean utility score is 0.536 (SD = 0.229). The distribution of candidate predictors, K10 and SOFAS, are summarised in Table \ref{tab:predrscors}. K10 was found to have the highest correlation with utility score both at baseline and follow-up followed by SOFAS.

\begin{table}

\caption{\label{tab:predrscors}Candidate predictors distribution parameters and correlations with AQoL-6D utility}
\centering
\begin{tabular}[t]{>{\raggedright\arraybackslash}p{14em}l>{\raggedright\arraybackslash}p{3em}>{\raggedright\arraybackslash}p{3em}l}
\toprule
\multicolumn{1}{c}{ } & \multicolumn{1}{c}{ } & \multicolumn{1}{c}{ } & \multicolumn{1}{c}{ } & \multicolumn{1}{c}{ } \\

 &  & (N = & 3998) & \textit{p}\\
\midrule
 & Mean (SD) & 28.569 & (8.343) & \\
\cmidrule{2-5}
 & Missing & 2.000 &  & \\
\cmidrule{2-5}
\multirow{-3}{14em}{\raggedright\arraybackslash \textbf{Kessler Psychological Distress Scale (10 Item) (10-50)}} & Correlation with AQOL-6D & -0.655 &  & 0.000\\
\cmidrule{1-5}
 & Mean (SD) & 64.821 & (14.937) & \\
\cmidrule{2-5}
 & Missing & 700.000 &  & \\
\cmidrule{2-5}
\multirow{-3}{14em}{\raggedright\arraybackslash \textbf{Social and Occupational Functioning Assessment Scale (0-100)}} & Correlation with AQOL-6D & 0.191 &  & 0.000\\
\bottomrule
\end{tabular}
\end{table}

\begin{figure}
\includegraphics[width=400px]{../../../Output/_Descriptives/combined_utl} \caption{Distribution of AQoL-6D domains}\label{fig:fig1}
\end{figure}

\hypertarget{performance-of-regression-models}{%
\subsection{Performance of regression models}\label{performance-of-regression-models}}

The 10-fold cross-validated model fitting index from TTU models using K10 are reported in Table \ref{tab:tenfoldolstb} in the Supplementary Material. Both GLM with Gaussian distribution and log link and OLS with complementary log log transformation were selected for further evaluation. Predictive ability of each candidate predictor using baseline data were also compared using 10-fold cross-validation.

Table \ref{tab:tenfoldglmtb} illustrates that K10 had the highest predictive ability followed by SOFAS.

The confounding effect of other participant characteristics when using the candidate predictors in predicting utility score were also evaluated. Days out of role, age, gender and education and employment were found to independently predict utility scores in models for both candidate predictors \emph{(p\textless0.01)}.

\hypertarget{utility-mapping-models-1}{%
\subsection{Utility mapping models}\label{utility-mapping-models-1}}

Regression coefficients of the baseline score and score changes (from baseline to follow-up) estimated in individual GLMM and LMM models are summarised in Table \ref{tab:cfscl}. Bayesian R\textsuperscript{2} and modelled residual standard deviations (SDs) from each model are reported. In both GLMM and LMM models, the prediction models using K10 had the highest R\textsuperscript{2} (0.438 and 0.609). R\textsuperscript{2} was between 0.082 and 0.438 for all GLMMs and between 0.428 and 0.609 for all LMMs.

\blandscape

\begin{longtable}[t]{ll>{\raggedright\arraybackslash}p{3em}>{\raggedright\arraybackslash}p{3em}>{\raggedright\arraybackslash}p{3em}>{\raggedright\arraybackslash}p{3em}lllll}
\caption{\label{tab:cfscl}Estimated coefficients from utility mapping models}\\
\toprule
\multicolumn{1}{c}{ } & \multicolumn{5}{c}{GLMM - Gaussian distribution and log link} & \multicolumn{5}{c}{LMM - complementary log log transformation} \\
\cmidrule(l{3pt}r{3pt}){2-6} \cmidrule(l{3pt}r{3pt}){7-11}
Parameter & Estimate & SE & CI (95\%) & R2 & Sigma & Estimate & SE & CI (95\%) & R2 & Sigma\\
\midrule
\endfirsthead
\caption[]{\label{tab:cfscl}Estimated coefficients from utility mapping models \textit{(continued)}}\\
\toprule
Parameter & Estimate & SE & CI (95\%) & R2 & Sigma & Estimate & SE & CI (95\%) & R2 & Sigma\\
\midrule
\endhead

\endfoot
\bottomrule
\multicolumn{11}{l}{\rule{0pt}{1em}\textit{ }}\\
\multicolumn{11}{l}{\rule{0pt}{1em}Note: The K10 and SOFAS parameters were first multiplied by 0.01.}\\
\endlastfoot
\textbf{K10 model} & \textbf{} & \textbf{} & \textbf{} & \textbf{0.438} & \textbf{0.171} & \textbf{} & \textbf{} & \textbf{} & \textbf{0.609} & \textbf{0.480}\\
\cmidrule{1-11}\pagebreak[0]
SD (Intercept) & 0.034 & 0.022 & 0.001, 0.079 &  &  & 0.304 & 0.164 & 0.016, 0.570 &  & \\
\cmidrule{1-11}\pagebreak[0]
Intercept & 0.280 & 0.015 & 0.249, 0.310 &  &  & 1.437 & 0.034 & 1.370, 1.504 &  & \\
\cmidrule{1-11}\pagebreak[0]
K10 scaled & -3.297 & 0.061 & -3.419, -3.177 &  &  & -6.114 & 0.114 & -6.339, -5.890 &  & \\
\cmidrule{1-11}\pagebreak[0]
\textbf{SOFAS model} & \textbf{} & \textbf{} & \textbf{} & \textbf{0.082} & \textbf{0.220} & \textbf{} & \textbf{} & \textbf{} & \textbf{0.428} & \textbf{0.570}\\
\cmidrule{1-11}\pagebreak[0]
SD (Intercept) & 0.067 & 0.044 & 0.003, 0.157 &  &  & 0.443 & 0.220 & 0.044, 0.740 &  & \\
\cmidrule{1-11}\pagebreak[0]
Intercept & -1.048 & 0.040 & -1.129, -0.972 &  &  & -0.931 & 0.061 & -1.053, -0.810 &  & \\
\cmidrule{1-11}\pagebreak[0]
SOFAS scaled & 0.653 & 0.060 & 0.539, 0.771 &  &  & 0.980 & 0.091 & 0.802, 1.163 &  & \\*
\end{longtable}

\elandscape

Distribution of observed and predicted utility scores and their association from GLMM (Gaussian distribution and log link) and LMM (complementary log log transformation) using K10 are plotted in Figure \ref{fig:fig2}.

We also evaluated models with cdaysoor, dage, dgender and dstudyingworking at baseline and cdaysoor, dage, dgender and dstudyingworking change from baseline added to psychological distress, functioning, clinical symptom and demographic predictors (see Tables \ref{tab:coefscovarstype1} and \ref{tab:coefscovarstype2}).

Detailed summaries of all models are available in the online data repository (see ``Availability of data and materials'').

\begin{figure}
\includegraphics[width=400px]{../../../Output/dens_and_sctr} \caption{Comparison of observed and predicted AQoL-6D score from longitudinal model using K10 (A) Density plots of observed and predicted utility scores (GLMM (Gaussian distribution and log link)) (B) Scatter plots of observed and predicted utility scores by timepoint (GLMM (Gaussian distribution and log link)) (C) Density plots of observed and predicted results (LMM (complementary log log transformation)) (D) Scatter plots of observed and predicted results by timepoint (LMM (complementary log log transformation))}\label{fig:fig2}
\end{figure}

\hypertarget{conclusions}{%
\section{Conclusions}\label{conclusions}}

Nothing should be concluded from this study as it is purely hypothetical.

\hypertarget{availability-of-data-and-materials}{%
\subsection*{Availability of data and materials}\label{availability-of-data-and-materials}}
\addcontentsline{toc}{subsection}{Availability of data and materials}

Detailed results in the form of catalogues of the models produced by this study and other supporting information are available in the online repository: \url{https://doi.org/10.7910/DVN/LYBMB0}

\hypertarget{ethics-approval}{%
\subsection*{Ethics approval}\label{ethics-approval}}
\addcontentsline{toc}{subsection}{Ethics approval}

The study was reviewed and granted approval by no-one.

\hypertarget{funding}{%
\subsection*{Funding}\label{funding}}
\addcontentsline{toc}{subsection}{Funding}

The study was funded by no-one.

\hypertarget{conflict-of-interest}{%
\subsection*{Conflict of Interest}\label{conflict-of-interest}}
\addcontentsline{toc}{subsection}{Conflict of Interest}

None declared

\newpage

\hypertarget{references}{%
\section*{References}\label{references}}
\addcontentsline{toc}{section}{References}

\hypertarget{refs}{}
\begin{CSLReferences}{0}{0}
\leavevmode\vadjust pre{\hypertarget{ref-TTUExtension}{}}%
\CSLLeftMargin{1. }%
\CSLRightInline{Hamilton M, Gao C. {ttu\_lng\_ss: Create a Draft Scientific Manuscript For A Utility Mapping Study} {[}Internet{]}. Zenodo; 2023. doi:\href{https://doi.org/10.5281/zenodo.5976987}{10.5281/zenodo.5976987}}

\leavevmode\vadjust pre{\hypertarget{ref-HamiltonGao2021}{}}%
\CSLLeftMargin{2. }%
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\end{CSLReferences}

\newpage
\appendix
\counterwithin{figure}{section}
\counterwithin{table}{section}

\hypertarget{supplementary-material}{%
\section{Supplementary Material}\label{supplementary-material}}

\hypertarget{additional-tables}{%
\subsection{Additional tables}\label{additional-tables}}

\begin{longtable}[t]{>{\raggedright\arraybackslash}p{20em}llllll}
\caption{\label{tab:tenfoldolstb}10-fold cross-validated model fitting index for different GLM and OLS models using K10 as predictor with the baseline data}\\
\toprule
\multicolumn{1}{c}{ } & \multicolumn{3}{c}{Training model fit} & \multicolumn{3}{c}{Testing model fit} \\
\cmidrule(l{3pt}r{3pt}){2-4} \cmidrule(l{3pt}r{3pt}){5-7}
Model & R2 & RMSE & MAE & R2 & RMSE & MAE\\
\midrule
\endfirsthead
\caption[]{\label{tab:tenfoldolstb}10-fold cross-validated model fitting index for different GLM and OLS models using K10 as predictor with the baseline data \textit{(continued)}}\\
\toprule
Model & R2 & RMSE & MAE & R2 & RMSE & MAE\\
\midrule
\endhead

\endfoot
\bottomrule
\multicolumn{7}{l}{\rule{0pt}{1em}\textit{ }}\\
\multicolumn{7}{l}{\rule{0pt}{1em}Results are averaged over ten folds. RMSE: Root Mean Squared Error; MAE: Mean Absolute Error}\\
\endlastfoot
\textbf{\textbf{OLS}} &  &  &  &  &  & \\
\cmidrule{1-7}\pagebreak[0]
\textbf{No transformation} & 0.429 & 0.173 & 0.141 & 0.428 & 0.173 & 0.141\\
\cmidrule{1-7}\pagebreak[0]
\textbf{Complementary log log transformation} & 0.426 & 0.174 & 0.140 & 0.425 & 0.174 & 0.140\\
\cmidrule{1-7}\pagebreak[0]
\textbf{Log transformation} & 0.408 & 0.176 & 0.143 & 0.407 & 0.176 & 0.143\\
\cmidrule{1-7}\pagebreak[0]
\textbf{Logit transformation} & 0.392 & 0.179 & 0.142 & 0.390 & 0.179 & 0.142\\
\cmidrule{1-7}\pagebreak[0]
\textbf{Log log transformation} & 0.344 & 0.186 & 0.146 & 0.342 & 0.186 & 0.146\\
\cmidrule{1-7}\pagebreak[0]
\textbf{\textbf{GLM}} &  &  &  &  &  & \\
\cmidrule{1-7}\pagebreak[0]
\textbf{Gaussian distribution and log link} & 0.433 & 0.173 & 0.140 & 0.432 & 0.173 & 0.140\\
\cmidrule{1-7}\pagebreak[0]
\textbf{Beta distribution and complementary log log link} & 0.431 & 0.173 & 0.140 & 0.430 & 0.173 & 0.140\\
\cmidrule{1-7}\pagebreak[0]
\textbf{Beta distribution and logit link} & 0.425 & 0.174 & 0.141 & 0.423 & 0.174 & 0.141\\*
\end{longtable}
\newpage

\begin{longtable}[t]{>{\raggedright\arraybackslash}p{20em}llllll}
\caption{\label{tab:tenfoldglmtb}10-fold cross-validated model fitting index for different candidate predictors estimated using GLM with Gaussian distribution and log link with the baseline data}\\
\toprule
\multicolumn{1}{c}{ } & \multicolumn{3}{c}{Training model fit} & \multicolumn{3}{c}{Testing model fit} \\
\cmidrule(l{3pt}r{3pt}){2-4} \cmidrule(l{3pt}r{3pt}){5-7}
Model & R2 & RMSE & MAE & R2 & RMSE & MAE\\
\midrule
\endfirsthead
\caption[]{\label{tab:tenfoldglmtb}10-fold cross-validated model fitting index for different candidate predictors estimated using GLM with Gaussian distribution and log link with the baseline data \textit{(continued)}}\\
\toprule
Model & R2 & RMSE & MAE & R2 & RMSE & MAE\\
\midrule
\endhead

\endfoot
\bottomrule
\multicolumn{7}{l}{\rule{0pt}{1em}\textit{ }}\\
\multicolumn{7}{l}{\rule{0pt}{1em}Results are averaged over ten folds. RMSE: Root Mean Squared Error; MAE: Mean Absolute Error}\\
\endlastfoot
\textbf{\textbf{K10}} & 0.433 & 0.173 & 0.140 & 0.432 & 0.173 & 0.140\\
\cmidrule{1-7}\pagebreak[0]
\textbf{\textbf{SOFAS}} & 0.041 & 0.225 & 0.187 & 0.040 & 0.225 & 0.187\\*
\end{longtable}

\newpage

\begin{longtable}[t]{>{\raggedright\arraybackslash}p{25em}lllll}
\caption{\label{tab:coefscovarstype1}Estimated coefficients from utility mapping models based on individual candidate predictors with days out of role, age and gender and education and employment using GLMM (Gaussian distribution and log link)}\\
\toprule
Parameter & Estimate & SE & CI (95\%) & R2 & Sigma\\
\midrule
\endfirsthead
\caption[]{\label{tab:coefscovarstype1}Estimated coefficients from utility mapping models based on individual candidate predictors with days out of role, age and gender and education and employment using GLMM (Gaussian distribution and log link) \textit{(continued)}}\\
\toprule
Parameter & Estimate & SE & CI (95\%) & R2 & Sigma\\
\midrule
\endhead

\endfoot
\bottomrule
\multicolumn{6}{l}{\rule{0pt}{1em}\textit{ }}\\
\multicolumn{6}{l}{\rule{0pt}{1em}Note: The K10 and SOFAS parameters were first multiplied by 0.01.}\\
\endlastfoot
\textbf{\textbf{K10 cdaysoor model}} & \textbf{} & \textbf{} & \textbf{} & \textbf{0.451} & \textbf{1.050}\\
\cmidrule{1-6}\pagebreak[0]
SD (Intercept) & 0.322 & 0.525 & 0.001, 1.499 &  & \\
\cmidrule{1-6}\pagebreak[0]
Intercept & 0.106 & 0.264 & -0.383,  0.303 &  & \\
\cmidrule{1-6}\pagebreak[0]
K10 scaled & -2.531 & 0.725 & -3.129, -1.380 &  & \\
\cmidrule{1-6}\pagebreak[0]
cdaysoor & -0.004 & 0.003 & -0.008,  0.003 &  & \\
\cmidrule{1-6}\pagebreak[0]
\textbf{\textbf{K10 dage model}} & \textbf{} & \textbf{} & \textbf{} & \textbf{0.442} & \textbf{0.171}\\
\cmidrule{1-6}\pagebreak[0]
SD (Intercept) & 0.038 & 0.023 & 0.002, 0.085 &  & \\
\cmidrule{1-6}\pagebreak[0]
Intercept & 0.361 & 0.027 & 0.309, 0.414 &  & \\
\cmidrule{1-6}\pagebreak[0]
K10 scaled & -3.268 & 0.060 & -3.385, -3.152 &  & \\
\cmidrule{1-6}\pagebreak[0]
dage & -0.005 & 0.001 & -0.008, -0.002 &  \vphantom{1} & \\
\cmidrule{1-6}\pagebreak[0]
\textbf{\textbf{K10 dgender model}} & \textbf{} & \textbf{} & \textbf{} & \textbf{0.440} & \textbf{0.171}\\
\cmidrule{1-6}\pagebreak[0]
SD (Intercept) & 0.035 & 0.022 & 0.002, 0.080 &  & \\
\cmidrule{1-6}\pagebreak[0]
Intercept & 0.258 & 0.017 & 0.225, 0.290 &  & \\
\cmidrule{1-6}\pagebreak[0]
K10 scaled & -3.262 & 0.061 & -3.379, -3.140 &  & \\
\cmidrule{1-6}\pagebreak[0]
dgenderMale & 0.031 & 0.010 & 0.011, 0.051 &  & \\
\cmidrule{1-6}\pagebreak[0]
dgenderOther & -0.015 & 0.038 & -0.089,  0.058 &  & \\
\cmidrule{1-6}\pagebreak[0]
\textbf{\textbf{K10 dstudyingworking model}} & \textbf{} & \textbf{} & \textbf{} & \textbf{0.440} & \textbf{0.171}\\
\cmidrule{1-6}\pagebreak[0]
SD (Intercept) & 0.035 & 0.022 & 0.001, 0.081 &  & \\
\cmidrule{1-6}\pagebreak[0]
Intercept & 0.237 & 0.019 & 0.199, 0.275 &  & \\
\cmidrule{1-6}\pagebreak[0]
K10 scaled & -3.287 & 0.062 & -3.409, -3.166 &  & \\
\cmidrule{1-6}\pagebreak[0]
dstudyingworkingBoth & 0.065 & 0.015 & 0.035, 0.095 &  & \\
\cmidrule{1-6}\pagebreak[0]
dstudyingworkingStudy & 0.044 & 0.014 & 0.017, 0.072 &  & \\
\cmidrule{1-6}\pagebreak[0]
dstudyingworkingWork & 0.041 & 0.017 & 0.008, 0.073 &  & \\
\cmidrule{1-6}\pagebreak[0]
\textbf{K10 cdaysoor 2 GLM GSN LOG} & \textbf{} & \textbf{} & \textbf{} & \textbf{0.477} & \textbf{1.297}\\
\cmidrule{1-6}\pagebreak[0]
SD (Intercept) & 0.471 & 0.577 & 0.001, 1.585 &  & \\
\cmidrule{1-6}\pagebreak[0]
Intercept & 5.271 & 6.931 & 0.335, 17.309 &  & \\
\cmidrule{1-6}\pagebreak[0]
K10 scaled & -2.002 & 1.009 & -3.087, -0.676 &  & \\
\cmidrule{1-6}\pagebreak[0]
cdaysoor & 0.002 & 0.018 & -0.006,  0.071 &  & \\
\cmidrule{1-6}\pagebreak[0]
dage & -0.249 & 0.375 & -0.891, -0.004 &  & \\
\cmidrule{1-6}\pagebreak[0]
\textbf{K10 cdaysoor 3 GLM GSN LOG} & \textbf{} & \textbf{} & \textbf{} & \textbf{0.464} & \textbf{0.716}\\
\cmidrule{1-6}\pagebreak[0]
SD (Intercept) & 1.542 & 2.537 & 0.004, 5.936 &  & \\
\cmidrule{1-6}\pagebreak[0]
Intercept & 0.500 & 0.643 & -0.015,  1.825 &  & \\
\cmidrule{1-6}\pagebreak[0]
K10 scaled & -2.008 & 1.012 & -3.095, -0.675 &  & \\
\cmidrule{1-6}\pagebreak[0]
cdaysoor & 0.003 & 0.019 & -0.006,  0.068 &  & \\
\cmidrule{1-6}\pagebreak[0]
dgenderMale & -0.367 & 0.429 & -0.989,  0.047 &  & \\
\cmidrule{1-6}\pagebreak[0]
dgenderOther & 0.681 & 0.709 & -0.088,  1.453 &  & \\
\cmidrule{1-6}\pagebreak[0]
\textbf{K10 cdaysoor 4 GLM GSN LOG} & \textbf{} & \textbf{} & \textbf{} & \textbf{0.455} & \textbf{0.171}\\
\cmidrule{1-6}\pagebreak[0]
SD (Intercept) & 0.841 & 1.416 & 0.001, 3.294 &  & \\
\cmidrule{1-6}\pagebreak[0]
Intercept & -0.158 & 0.688 & -1.945,  0.274 &  & \\
\cmidrule{1-6}\pagebreak[0]
K10 scaled & -2.362 & 1.006 & -3.123, -0.674 &  & \\
\cmidrule{1-6}\pagebreak[0]
cdaysoor & 0.003 & 0.020 & -0.008,  0.069 &  & \\
\cmidrule{1-6}\pagebreak[0]
dstudyingworkingBoth & -0.210 & 0.452 & -0.991,  0.082 &  & \\
\cmidrule{1-6}\pagebreak[0]
dstudyingworkingStudy & 0.373 & 0.556 & 0.016, 1.325 &  & \\
\cmidrule{1-6}\pagebreak[0]
dstudyingworkingWork & -0.104 & 0.262 & -0.526,  0.067 &  & \\
\cmidrule{1-6}\pagebreak[0]
\textbf{K10 dage 2 GLM GSN LOG} & \textbf{} & \textbf{} & \textbf{} & \textbf{0.441} & \textbf{0.171}\\
\cmidrule{1-6}\pagebreak[0]
SD (Intercept) & 0.035 & 0.022 & 0.002, 0.081 &  & \\
\cmidrule{1-6}\pagebreak[0]
Intercept & 0.340 & 0.028 & 0.285, 0.395 &  & \\
\cmidrule{1-6}\pagebreak[0]
K10 scaled & -3.230 & 0.062 & -3.351, -3.109 &  & \\
\cmidrule{1-6}\pagebreak[0]
dage & -0.005 & 0.001 & -0.008, -0.002 &  & \\
\cmidrule{1-6}\pagebreak[0]
dgenderMale & 0.032 & 0.010 & 0.012, 0.053 &  & \\
\cmidrule{1-6}\pagebreak[0]
dgenderOther & -0.005 & 0.039 & -0.084,  0.069 &  & \\
\cmidrule{1-6}\pagebreak[0]
\textbf{K10 dage 3 GLM GSN LOG} & \textbf{} & \textbf{} & \textbf{} & \textbf{0.443} & \textbf{0.170}\\
\cmidrule{1-6}\pagebreak[0]
SD (Intercept) & 0.036 & 0.022 & 0.002, 0.082 &  & \\
\cmidrule{1-6}\pagebreak[0]
Intercept & 0.354 & 0.033 & 0.290, 0.420 &  & \\
\cmidrule{1-6}\pagebreak[0]
K10 scaled & -3.253 & 0.062 & -3.370, -3.131 &  & \\
\cmidrule{1-6}\pagebreak[0]
dage & -0.007 & 0.002 & -0.010, -0.004 &  & \\
\cmidrule{1-6}\pagebreak[0]
dstudyingworkingBoth & 0.069 & 0.016 & 0.039, 0.100 &  & \\
\cmidrule{1-6}\pagebreak[0]
dstudyingworkingStudy & 0.028 & 0.015 & 0.000, 0.057 &  & \\
\cmidrule{1-6}\pagebreak[0]
dstudyingworkingWork & 0.057 & 0.017 & 0.024, 0.091 &  & \\
\cmidrule{1-6}\pagebreak[0]
\textbf{K10 dgender 2 GLM GSN LOG} & \textbf{} & \textbf{} & \textbf{} & \textbf{0.443} & \textbf{0.170}\\
\cmidrule{1-6}\pagebreak[0]
SD (Intercept) & 0.037 & 0.023 & 0.002, 0.083 &  & \\
\cmidrule{1-6}\pagebreak[0]
Intercept & 0.206 & 0.021 & 0.165, 0.247 &  & \\
\cmidrule{1-6}\pagebreak[0]
K10 scaled & -3.241 & 0.062 & -3.365, -3.119 &  & \\
\cmidrule{1-6}\pagebreak[0]
dgenderMale & 0.038 & 0.010 & 0.018, 0.058 &  & \\
\cmidrule{1-6}\pagebreak[0]
dgenderOther & -0.015 & 0.038 & -0.089,  0.056 &  & \\
\cmidrule{1-6}\pagebreak[0]
dstudyingworkingBoth & 0.071 & 0.016 & 0.041, 0.102 &  & \\
\cmidrule{1-6}\pagebreak[0]
dstudyingworkingStudy & 0.049 & 0.014 & 0.021, 0.077 &  & \\
\cmidrule{1-6}\pagebreak[0]
dstudyingworkingWork & 0.045 & 0.017 & 0.012, 0.078 &  & \\
\cmidrule{1-6}\pagebreak[0]
\textbf{\textbf{SOFAS cdaysoor model}} & \textbf{} & \textbf{} & \textbf{} & \textbf{0.264} & \textbf{1.181}\\
\cmidrule{1-6}\pagebreak[0]
SD (Intercept) & 0.298 & 0.415 & 0.002, 1.218 &  & \\
\cmidrule{1-6}\pagebreak[0]
Intercept & -0.414 & 0.470 & -0.815,  0.429 &  & \\
\cmidrule{1-6}\pagebreak[0]
SOFAS scaled & -0.086 & 0.788 & -1.381,  0.578 &  & \\
\cmidrule{1-6}\pagebreak[0]
cdaysoor & -0.011 & 0.004 & -0.015, -0.001 &  & \\
\cmidrule{1-6}\pagebreak[0]
\textbf{\textbf{SOFAS dage model}} & \textbf{} & \textbf{} & \textbf{} & \textbf{0.091} & \textbf{0.219}\\
\cmidrule{1-6}\pagebreak[0]
SD (Intercept) & 0.064 & 0.044 & 0.003, 0.164 &  & \\
\cmidrule{1-6}\pagebreak[0]
Intercept & -0.806 & 0.055 & -0.914, -0.700 &  & \\
\cmidrule{1-6}\pagebreak[0]
SOFAS scaled & 0.641 & 0.058 & 0.530, 0.757 &  & \\
\cmidrule{1-6}\pagebreak[0]
dage & -0.013 & 0.002 & -0.018, -0.009 &  & \\
\cmidrule{1-6}\pagebreak[0]
\textbf{\textbf{SOFAS dgender model}} & \textbf{} & \textbf{} & \textbf{} & \textbf{0.104} & \textbf{0.218}\\
\cmidrule{1-6}\pagebreak[0]
SD (Intercept) & 0.073 & 0.045 & 0.003, 0.161 &  & \\
\cmidrule{1-6}\pagebreak[0]
Intercept & -1.076 & 0.039 & -1.153, -1.001 &  & \\
\cmidrule{1-6}\pagebreak[0]
SOFAS scaled & 0.634 & 0.058 & 0.525, 0.747 &  & \\
\cmidrule{1-6}\pagebreak[0]
dgenderMale & 0.109 & 0.015 & 0.080, 0.137 &  & \\
\cmidrule{1-6}\pagebreak[0]
dgenderOther & -0.116 & 0.059 & -0.239, -0.003 &  & \\
\cmidrule{1-6}\pagebreak[0]
\textbf{\textbf{SOFAS dstudyingworking model}} & \textbf{} & \textbf{} & \textbf{} & \textbf{0.077} & \textbf{0.221}\\
\cmidrule{1-6}\pagebreak[0]
SD (Intercept) & 0.055 & 0.040 & 0.002, 0.146 &  & \\
\cmidrule{1-6}\pagebreak[0]
Intercept & -1.083 & 0.043 & -1.167, -1.000 &  & \\
\cmidrule{1-6}\pagebreak[0]
SOFAS scaled & 0.644 & 0.061 & 0.526, 0.763 &  & \\
\cmidrule{1-6}\pagebreak[0]
dstudyingworkingBoth & 0.058 & 0.023 & 0.015, 0.102 &  & \\
\cmidrule{1-6}\pagebreak[0]
dstudyingworkingStudy & 0.066 & 0.021 & 0.026, 0.107 &  & \\
\cmidrule{1-6}\pagebreak[0]
dstudyingworkingWork & 0.016 & 0.025 & -0.032,  0.065 &  & \\
\cmidrule{1-6}\pagebreak[0]
\textbf{SOFAS cdaysoor 2 GLM GSN LOG} & \textbf{} & \textbf{} & \textbf{} & \textbf{0.344} & \textbf{1.207}\\
\cmidrule{1-6}\pagebreak[0]
SD (Intercept) & 0.597 & 0.777 & 0.002, 1.924 &  & \\
\cmidrule{1-6}\pagebreak[0]
Intercept & 6.578 & 7.505 & -0.605, 17.516 &  & \\
\cmidrule{1-6}\pagebreak[0]
SOFAS scaled & -0.274 & 0.796 & -1.381,  0.564 &  & \\
\cmidrule{1-6}\pagebreak[0]
cdaysoor & 0.000 & 0.024 & -0.014,  0.076 &  & \\
\cmidrule{1-6}\pagebreak[0]
dage & -0.343 & 0.366 & -0.898, -0.010 &  & \\
\cmidrule{1-6}\pagebreak[0]
\textbf{SOFAS cdaysoor 3 GLM GSN LOG} & \textbf{} & \textbf{} & \textbf{} & \textbf{0.329} & \textbf{0.745}\\
\cmidrule{1-6}\pagebreak[0]
SD (Intercept) & 0.713 & 1.158 & 0.003, 3.439 &  & \\
\cmidrule{1-6}\pagebreak[0]
Intercept & 0.301 & 1.356 & -0.849,  2.535 &  & \\
\cmidrule{1-6}\pagebreak[0]
SOFAS scaled & -0.273 & 0.792 & -1.375,  0.564 &  & \\
\cmidrule{1-6}\pagebreak[0]
cdaysoor & -0.009 & 0.012 & -0.013, -0.002 &  & \\
\cmidrule{1-6}\pagebreak[0]
dgenderMale & -0.338 & 0.460 & -0.989,  0.117 &  & \\
\cmidrule{1-6}\pagebreak[0]
dgenderOther & 0.638 & 0.758 & -0.212,  1.463 &  & \\
\cmidrule{1-6}\pagebreak[0]
\textbf{SOFAS cdaysoor 4 GLM GSN LOG} & \textbf{} & \textbf{} & \textbf{} & \textbf{0.262} & \textbf{0.198}\\
\cmidrule{1-6}\pagebreak[0]
SD (Intercept) & 0.860 & 1.427 & 0.002, 3.332 &  & \\
\cmidrule{1-6}\pagebreak[0]
Intercept & -0.935 & 0.377 & -1.961, -0.643 &  & \\
\cmidrule{1-6}\pagebreak[0]
SOFAS scaled & 0.187 & 0.516 & -0.673,  0.589 &  & \\
\cmidrule{1-6}\pagebreak[0]
cdaysoor & 0.004 & 0.032 & -0.014,  0.085 &  & \\
\cmidrule{1-6}\pagebreak[0]
dstudyingworkingBoth & -0.237 & 0.437 & -0.991,  0.059 &  & \\
\cmidrule{1-6}\pagebreak[0]
dstudyingworkingStudy & 0.365 & 0.556 & 0.004, 1.324 &  & \\
\cmidrule{1-6}\pagebreak[0]
dstudyingworkingWork & -0.154 & 0.224 & -0.527,  0.016 &  & \\
\cmidrule{1-6}\pagebreak[0]
\textbf{SOFAS dage 2 GLM GSN LOG} & \textbf{} & \textbf{} & \textbf{} & \textbf{0.114} & \textbf{0.217}\\
\cmidrule{1-6}\pagebreak[0]
SD (Intercept) & 0.070 & 0.044 & 0.003, 0.155 &  & \\
\cmidrule{1-6}\pagebreak[0]
Intercept & -0.825 & 0.054 & -0.934, -0.720 &  & \\
\cmidrule{1-6}\pagebreak[0]
SOFAS scaled & 0.619 & 0.058 & 0.507, 0.734 &  & \\
\cmidrule{1-6}\pagebreak[0]
dage & -0.014 & 0.002 & -0.018, -0.010 &  & \\
\cmidrule{1-6}\pagebreak[0]
dgenderMale & 0.114 & 0.014 & 0.085, 0.142 &  & \\
\cmidrule{1-6}\pagebreak[0]
dgenderOther & -0.089 & 0.058 & -0.205,  0.021 &  & \\
\cmidrule{1-6}\pagebreak[0]
\textbf{SOFAS dage 3 GLM GSN LOG} & \textbf{} & \textbf{} & \textbf{} & \textbf{0.092} & \textbf{0.219}\\
\cmidrule{1-6}\pagebreak[0]
SD (Intercept) & 0.063 & 0.041 & 0.003, 0.149 &  & \\
\cmidrule{1-6}\pagebreak[0]
Intercept & -0.813 & 0.063 & -0.939, -0.686 &  & \\
\cmidrule{1-6}\pagebreak[0]
SOFAS scaled & 0.622 & 0.060 & 0.506, 0.740 &  & \\
\cmidrule{1-6}\pagebreak[0]
dage & -0.014 & 0.002 & -0.019, -0.009 &  & \\
\cmidrule{1-6}\pagebreak[0]
dstudyingworkingBoth & 0.061 & 0.022 & 0.018, 0.106 &  & \\
\cmidrule{1-6}\pagebreak[0]
dstudyingworkingStudy & 0.034 & 0.021 & -0.006,  0.076 &  & \\
\cmidrule{1-6}\pagebreak[0]
dstudyingworkingWork & 0.046 & 0.025 & -0.003,  0.095 &  & \\
\cmidrule{1-6}\pagebreak[0]
\textbf{SOFAS dgender 2 GLM GSN LOG} & \textbf{} & \textbf{} & \textbf{} & \textbf{0.105} & \textbf{0.218}\\
\cmidrule{1-6}\pagebreak[0]
SD (Intercept) & 0.066 & 0.044 & 0.003, 0.158 &  & \\
\cmidrule{1-6}\pagebreak[0]
Intercept & -1.121 & 0.042 & -1.204, -1.040 &  & \\
\cmidrule{1-6}\pagebreak[0]
SOFAS scaled & 0.617 & 0.058 & 0.503, 0.731 &  & \\
\cmidrule{1-6}\pagebreak[0]
dgenderMale & 0.116 & 0.015 & 0.087, 0.146 &  & \\
\cmidrule{1-6}\pagebreak[0]
dgenderOther & -0.114 & 0.060 & -0.236, -0.001 &  & \\
\cmidrule{1-6}\pagebreak[0]
dstudyingworkingBoth & 0.078 & 0.023 & 0.035, 0.123 &  & \\
\cmidrule{1-6}\pagebreak[0]
dstudyingworkingStudy & 0.081 & 0.021 & 0.041, 0.121 &  & \\
\cmidrule{1-6}\pagebreak[0]
dstudyingworkingWork & 0.030 & 0.024 & -0.018,  0.077 &  & \\*
\end{longtable}

\newpage

\begin{longtable}[t]{>{\raggedright\arraybackslash}p{25em}lllll}
\caption{\label{tab:coefscovarstype2}Estimated coefficients from utility mapping models based on individual candidate predictors with days out of role, age and gender and education and employment using LMM (complementary log log transformation)}\\
\toprule
Parameter & Estimate & SE & CI (95\%) & R2 & Sigma\\
\midrule
\endfirsthead
\caption[]{\label{tab:coefscovarstype2}Estimated coefficients from utility mapping models based on individual candidate predictors with days out of role, age and gender and education and employment using LMM (complementary log log transformation) \textit{(continued)}}\\
\toprule
Parameter & Estimate & SE & CI (95\%) & R2 & Sigma\\
\midrule
\endhead

\endfoot
\bottomrule
\multicolumn{6}{l}{\rule{0pt}{1em}\textit{ }}\\
\multicolumn{6}{l}{\rule{0pt}{1em}Note: The K10 and SOFAS parameters were first multiplied by 0.01.}\\
\endlastfoot
\textbf{\textbf{K10 cdaysoor model}} & \textbf{} & \textbf{} & \textbf{} & \textbf{0.625} & \textbf{0.470}\\
\cmidrule{1-6}\pagebreak[0]
SD (Intercept) & 0.307 & 0.156 & 0.024, 0.543 &  & \\
\cmidrule{1-6}\pagebreak[0]
Intercept & 1.437 & 0.033 & 1.373, 1.502 &  & \\
\cmidrule{1-6}\pagebreak[0]
K10 scaled & -5.619 & 0.120 & -5.854, -5.381 &  & \\
\cmidrule{1-6}\pagebreak[0]
cdaysoor & -0.009 & 0.001 & -0.011, -0.007 &  \vphantom{1} & \\
\cmidrule{1-6}\pagebreak[0]
\textbf{\textbf{K10 dage model}} & \textbf{} & \textbf{} & \textbf{} & \textbf{0.588} & \textbf{0.498}\\
\cmidrule{1-6}\pagebreak[0]
SD (Intercept) & 0.277 & 0.164 & 0.013, 0.517 &  & \\
\cmidrule{1-6}\pagebreak[0]
Intercept & 1.682 & 0.056 & 1.571, 1.795 &  & \\
\cmidrule{1-6}\pagebreak[0]
K10 scaled & -6.063 & 0.114 & -6.285, -5.840 &  & \\
\cmidrule{1-6}\pagebreak[0]
dage & -0.015 & 0.003 & -0.020, -0.009 &  & \\
\cmidrule{1-6}\pagebreak[0]
\textbf{\textbf{K10 dgender model}} & \textbf{} & \textbf{} & \textbf{} & \textbf{0.611} & \textbf{0.482}\\
\cmidrule{1-6}\pagebreak[0]
SD (Intercept) & 0.310 & 0.151 & 0.020, 0.552 &  & \\
\cmidrule{1-6}\pagebreak[0]
Intercept & 1.391 & 0.037 & 1.318, 1.461 &  & \\
\cmidrule{1-6}\pagebreak[0]
K10 scaled & -6.042 & 0.117 & -6.269, -5.807 &  & \\
\cmidrule{1-6}\pagebreak[0]
dgenderMale & 0.071 & 0.020 & 0.032, 0.112 &  & \\
\cmidrule{1-6}\pagebreak[0]
dgenderOther & -0.032 & 0.064 & -0.158,  0.095 &  & \\
\cmidrule{1-6}\pagebreak[0]
\textbf{\textbf{K10 dstudyingworking model}} & \textbf{} & \textbf{} & \textbf{} & \textbf{0.754} & \textbf{0.365}\\
\cmidrule{1-6}\pagebreak[0]
SD (Intercept) & 0.428 & 0.156 & 0.025, 0.586 &  & \\
\cmidrule{1-6}\pagebreak[0]
Intercept & 1.350 & 0.039 & 1.273, 1.429 &  & \\
\cmidrule{1-6}\pagebreak[0]
K10 scaled & -6.111 & 0.114 & -6.337, -5.888 &  & \\
\cmidrule{1-6}\pagebreak[0]
dstudyingworkingBoth & 0.143 & 0.029 & 0.087, 0.198 &  & \\
\cmidrule{1-6}\pagebreak[0]
dstudyingworkingStudy & 0.092 & 0.026 & 0.042, 0.143 &  & \\
\cmidrule{1-6}\pagebreak[0]
dstudyingworkingWork & 0.088 & 0.030 & 0.030, 0.149 &  & \\
\cmidrule{1-6}\pagebreak[0]
\textbf{K10 cdaysoor 2 OLS CLL} & \textbf{} & \textbf{} & \textbf{} & \textbf{0.561} & \textbf{0.518}\\
\cmidrule{1-6}\pagebreak[0]
SD (Intercept) & 0.236 & 0.140 & 0.013, 0.490 &  & \\
\cmidrule{1-6}\pagebreak[0]
Intercept & 1.708 & 0.056 & 1.598, 1.818 &  & \\
\cmidrule{1-6}\pagebreak[0]
K10 scaled & -5.547 & 0.122 & -5.786, -5.306 &  & \\
\cmidrule{1-6}\pagebreak[0]
cdaysoor & -0.009 & 0.001 & -0.011, -0.008 &  & \\
\cmidrule{1-6}\pagebreak[0]
dage & -0.016 & 0.003 & -0.022, -0.011 &  & \\
\cmidrule{1-6}\pagebreak[0]
\textbf{K10 cdaysoor 3 OLS CLL} & \textbf{} & \textbf{} & \textbf{} & \textbf{0.630} & \textbf{0.470}\\
\cmidrule{1-6}\pagebreak[0]
SD (Intercept) & 0.317 & 0.142 & 0.032, 0.519 &  & \\
\cmidrule{1-6}\pagebreak[0]
Intercept & 1.390 & 0.036 & 1.321, 1.461 &  & \\
\cmidrule{1-6}\pagebreak[0]
K10 scaled & -5.544 & 0.123 & -5.783, -5.302 &  & \\
\cmidrule{1-6}\pagebreak[0]
cdaysoor & -0.009 & 0.001 & -0.011, -0.007 &  & \\
\cmidrule{1-6}\pagebreak[0]
dgenderMale & 0.074 & 0.020 & 0.034, 0.114 &  & \\
\cmidrule{1-6}\pagebreak[0]
dgenderOther & -0.042 & 0.064 & -0.168,  0.084 &  & \\
\cmidrule{1-6}\pagebreak[0]
\textbf{K10 cdaysoor 4 OLS CLL} & \textbf{} & \textbf{} & \textbf{} & \textbf{0.605} & \textbf{0.488}\\
\cmidrule{1-6}\pagebreak[0]
SD (Intercept) & 0.287 & 0.149 & 0.019, 0.516 &  & \\
\cmidrule{1-6}\pagebreak[0]
Intercept & 1.369 & 0.039 & 1.293, 1.445 &  & \\
\cmidrule{1-6}\pagebreak[0]
K10 scaled & -5.632 & 0.123 & -5.872, -5.393 &  & \\
\cmidrule{1-6}\pagebreak[0]
cdaysoor & -0.009 & 0.001 & -0.010, -0.007 &  & \\
\cmidrule{1-6}\pagebreak[0]
dstudyingworkingBoth & 0.109 & 0.029 & 0.052, 0.163 &  & \\
\cmidrule{1-6}\pagebreak[0]
dstudyingworkingStudy & 0.081 & 0.026 & 0.031, 0.132 &  & \\
\cmidrule{1-6}\pagebreak[0]
dstudyingworkingWork & 0.052 & 0.030 & -0.007,  0.111 &  & \\
\cmidrule{1-6}\pagebreak[0]
\textbf{K10 dage 2 OLS CLL} & \textbf{} & \textbf{} & \textbf{} & \textbf{0.715} & \textbf{0.400}\\
\cmidrule{1-6}\pagebreak[0]
SD (Intercept) & 0.395 & 0.161 & 0.042, 0.573 &  & \\
\cmidrule{1-6}\pagebreak[0]
Intercept & 1.641 & 0.058 & 1.528, 1.755 &  & \\
\cmidrule{1-6}\pagebreak[0]
K10 scaled & -5.994 & 0.116 & -6.222, -5.766 &  & \\
\cmidrule{1-6}\pagebreak[0]
dage & -0.015 & 0.003 & -0.020, -0.010 &  & \\
\cmidrule{1-6}\pagebreak[0]
dgenderMale & 0.077 & 0.020 & 0.037, 0.114 &  & \\
\cmidrule{1-6}\pagebreak[0]
dgenderOther & -0.006 & 0.065 & -0.129,  0.119 &  & \\
\cmidrule{1-6}\pagebreak[0]
\textbf{K10 dage 3 OLS CLL} & \textbf{} & \textbf{} & \textbf{} & \textbf{0.640} & \textbf{0.457}\\
\cmidrule{1-6}\pagebreak[0]
SD (Intercept) & 0.314 & 0.186 & 0.012, 0.539 &  & \\
\cmidrule{1-6}\pagebreak[0]
Intercept & 1.687 & 0.067 & 1.555, 1.818 &  & \\
\cmidrule{1-6}\pagebreak[0]
K10 scaled & -6.053 & 0.116 & -6.282, -5.824 &  & \\
\cmidrule{1-6}\pagebreak[0]
dage & -0.019 & 0.003 & -0.026, -0.013 &  & \\
\cmidrule{1-6}\pagebreak[0]
dstudyingworkingBoth & 0.146 & 0.030 & 0.087, 0.203 &  & \\
\cmidrule{1-6}\pagebreak[0]
dstudyingworkingStudy & 0.045 & 0.028 & -0.010,  0.099 &  & \\
\cmidrule{1-6}\pagebreak[0]
dstudyingworkingWork & 0.128 & 0.032 & 0.066, 0.191 &  & \\
\cmidrule{1-6}\pagebreak[0]
\textbf{K10 dgender 2 OLS CLL} & \textbf{} & \textbf{} & \textbf{} & \textbf{0.568} & \textbf{0.512}\\
\cmidrule{1-6}\pagebreak[0]
SD (Intercept) & 0.264 & 0.142 & 0.016, 0.509 &  & \\
\cmidrule{1-6}\pagebreak[0]
Intercept & 1.287 & 0.042 & 1.203, 1.369 &  & \\
\cmidrule{1-6}\pagebreak[0]
K10 scaled & -6.026 & 0.117 & -6.253, -5.797 &  & \\
\cmidrule{1-6}\pagebreak[0]
dgenderMale & 0.085 & 0.020 & 0.046, 0.125 &  & \\
\cmidrule{1-6}\pagebreak[0]
dgenderOther & -0.029 & 0.064 & -0.151,  0.097 &  & \\
\cmidrule{1-6}\pagebreak[0]
dstudyingworkingBoth & 0.156 & 0.030 & 0.099, 0.214 &  & \\
\cmidrule{1-6}\pagebreak[0]
dstudyingworkingStudy & 0.103 & 0.027 & 0.050, 0.156 &  & \\
\cmidrule{1-6}\pagebreak[0]
dstudyingworkingWork & 0.098 & 0.031 & 0.037, 0.160 &  & \\
\cmidrule{1-6}\pagebreak[0]
\textbf{\textbf{SOFAS cdaysoor model}} & \textbf{} & \textbf{} & \textbf{} & \textbf{0.547} & \textbf{0.514}\\
\cmidrule{1-6}\pagebreak[0]
SD (Intercept) & 0.465 & 0.181 & 0.044, 0.673 &  & \\
\cmidrule{1-6}\pagebreak[0]
Intercept & -0.464 & 0.060 & -0.583, -0.344 &  & \\
\cmidrule{1-6}\pagebreak[0]
SOFAS scaled & 0.777 & 0.085 & 0.610, 0.944 &  & \\
\cmidrule{1-6}\pagebreak[0]
cdaysoor & -0.021 & 0.001 & -0.023, -0.019 &  \vphantom{3} & \\
\cmidrule{1-6}\pagebreak[0]
\textbf{\textbf{SOFAS dage model}} & \textbf{} & \textbf{} & \textbf{} & \textbf{0.523} & \textbf{0.506}\\
\cmidrule{1-6}\pagebreak[0]
SD (Intercept) & 0.488 & 0.242 & 0.019, 0.759 &  & \\
\cmidrule{1-6}\pagebreak[0]
Intercept & -0.462 & 0.091 & -0.643, -0.286 &  & \\
\cmidrule{1-6}\pagebreak[0]
SOFAS scaled & 0.962 & 0.089 & 0.788, 1.137 &  & \\
\cmidrule{1-6}\pagebreak[0]
dage & -0.026 & 0.004 & -0.033, -0.019 &  & \\
\cmidrule{1-6}\pagebreak[0]
\textbf{\textbf{SOFAS dgender model}} & \textbf{} & \textbf{} & \textbf{} & \textbf{0.290} & \textbf{0.655}\\
\cmidrule{1-6}\pagebreak[0]
SD (Intercept) & 0.328 & 0.200 & 0.013, 0.668 &  & \\
\cmidrule{1-6}\pagebreak[0]
Intercept & -0.995 & 0.061 & -1.115, -0.876 &  & \\
\cmidrule{1-6}\pagebreak[0]
SOFAS scaled & 0.967 & 0.090 & 0.789, 1.145 &  & \\
\cmidrule{1-6}\pagebreak[0]
dgenderMale & 0.210 & 0.028 & 0.155, 0.264 &  & \\
\cmidrule{1-6}\pagebreak[0]
dgenderOther & -0.204 & 0.094 & -0.388, -0.019 &  & \\
\cmidrule{1-6}\pagebreak[0]
\textbf{\textbf{SOFAS dstudyingworking model}} & \textbf{} & \textbf{} & \textbf{} & \textbf{0.616} & \textbf{0.463}\\
\cmidrule{1-6}\pagebreak[0]
SD (Intercept) & 0.576 & 0.170 & 0.118, 0.745 &  & \\
\cmidrule{1-6}\pagebreak[0]
Intercept & -0.999 & 0.065 & -1.127, -0.871 &  & \\
\cmidrule{1-6}\pagebreak[0]
SOFAS scaled & 0.961 & 0.091 & 0.784, 1.140 &  & \\
\cmidrule{1-6}\pagebreak[0]
dstudyingworkingBoth & 0.123 & 0.042 & 0.042, 0.206 &  & \\
\cmidrule{1-6}\pagebreak[0]
dstudyingworkingStudy & 0.120 & 0.037 & 0.048, 0.195 &  & \\
\cmidrule{1-6}\pagebreak[0]
dstudyingworkingWork & 0.042 & 0.044 & -0.042,  0.130 &  & \\
\cmidrule{1-6}\pagebreak[0]
\textbf{SOFAS cdaysoor 2 OLS CLL} & \textbf{} & \textbf{} & \textbf{} & \textbf{0.541} & \textbf{0.499}\\
\cmidrule{1-6}\pagebreak[0]
SD (Intercept) & 0.435 & 0.218 & 0.032, 0.710 &  & \\
\cmidrule{1-6}\pagebreak[0]
Intercept & 0.029 & 0.092 & -0.149,  0.210 &  & \\
\cmidrule{1-6}\pagebreak[0]
SOFAS scaled & 0.751 & 0.087 & 0.577, 0.922 &  & \\
\cmidrule{1-6}\pagebreak[0]
cdaysoor & -0.021 & 0.001 & -0.023, -0.019 &  \vphantom{2} & \\
\cmidrule{1-6}\pagebreak[0]
dage & -0.027 & 0.004 & -0.034, -0.020 &  & \\
\cmidrule{1-6}\pagebreak[0]
\textbf{SOFAS cdaysoor 3 OLS CLL} & \textbf{} & \textbf{} & \textbf{} & \textbf{0.564} & \textbf{0.458}\\
\cmidrule{1-6}\pagebreak[0]
SD (Intercept) & 0.427 & 0.261 & 0.007, 0.724 &  & \\
\cmidrule{1-6}\pagebreak[0]
Intercept & -0.524 & 0.062 & -0.642, -0.403 &  & \\
\cmidrule{1-6}\pagebreak[0]
SOFAS scaled & 0.760 & 0.087 & 0.587, 0.930 &  & \\
\cmidrule{1-6}\pagebreak[0]
cdaysoor & -0.021 & 0.001 & -0.023, -0.019 &  \vphantom{1} & \\
\cmidrule{1-6}\pagebreak[0]
dgenderMale & 0.193 & 0.026 & 0.142, 0.243 &  & \\
\cmidrule{1-6}\pagebreak[0]
dgenderOther & -0.198 & 0.091 & -0.373, -0.020 &  & \\
\cmidrule{1-6}\pagebreak[0]
\textbf{SOFAS cdaysoor 4 OLS CLL} & \textbf{} & \textbf{} & \textbf{} & \textbf{0.622} & \textbf{0.455}\\
\cmidrule{1-6}\pagebreak[0]
SD (Intercept) & 0.513 & 0.179 & 0.075, 0.719 &  & \\
\cmidrule{1-6}\pagebreak[0]
Intercept & -0.490 & 0.066 & -0.617, -0.363 &  & \\
\cmidrule{1-6}\pagebreak[0]
SOFAS scaled & 0.771 & 0.085 & 0.605, 0.939 &  & \\
\cmidrule{1-6}\pagebreak[0]
cdaysoor & -0.021 & 0.001 & -0.023, -0.019 &  & \\
\cmidrule{1-6}\pagebreak[0]
dstudyingworkingBoth & 0.039 & 0.039 & -0.039,  0.115 &  & \\
\cmidrule{1-6}\pagebreak[0]
dstudyingworkingStudy & 0.084 & 0.035 & 0.014, 0.153 &  & \\
\cmidrule{1-6}\pagebreak[0]
dstudyingworkingWork & -0.053 & 0.042 & -0.136,  0.030 &  & \\
\cmidrule{1-6}\pagebreak[0]
\textbf{SOFAS dage 2 OLS CLL} & \textbf{} & \textbf{} & \textbf{} & \textbf{0.515} & \textbf{0.513}\\
\cmidrule{1-6}\pagebreak[0]
SD (Intercept) & 0.483 & 0.215 & 0.035, 0.756 &  & \\
\cmidrule{1-6}\pagebreak[0]
Intercept & -0.518 & 0.091 & -0.695, -0.339 &  & \\
\cmidrule{1-6}\pagebreak[0]
SOFAS scaled & 0.945 & 0.089 & 0.772, 1.118 &  & \\
\cmidrule{1-6}\pagebreak[0]
dage & -0.026 & 0.004 & -0.034, -0.019 &  & \\
\cmidrule{1-6}\pagebreak[0]
dgenderMale & 0.215 & 0.028 & 0.162, 0.270 &  & \\
\cmidrule{1-6}\pagebreak[0]
dgenderOther & -0.157 & 0.094 & -0.341,  0.022 &  & \\
\cmidrule{1-6}\pagebreak[0]
\textbf{SOFAS dage 3 OLS CLL} & \textbf{} & \textbf{} & \textbf{} & \textbf{0.442} & \textbf{0.557}\\
\cmidrule{1-6}\pagebreak[0]
SD (Intercept) & 0.443 & 0.218 & 0.038, 0.758 &  & \\
\cmidrule{1-6}\pagebreak[0]
Intercept & -0.466 & 0.108 & -0.667, -0.254 &  & \\
\cmidrule{1-6}\pagebreak[0]
SOFAS scaled & 0.933 & 0.089 & 0.762, 1.114 &  & \\
\cmidrule{1-6}\pagebreak[0]
dage & -0.028 & 0.005 & -0.038, -0.019 &  & \\
\cmidrule{1-6}\pagebreak[0]
dstudyingworkingBoth & 0.125 & 0.041 & 0.047, 0.207 &  & \\
\cmidrule{1-6}\pagebreak[0]
dstudyingworkingStudy & 0.050 & 0.039 & -0.021,  0.127 &  & \\
\cmidrule{1-6}\pagebreak[0]
dstudyingworkingWork & 0.098 & 0.047 & 0.007, 0.186 &  & \\
\cmidrule{1-6}\pagebreak[0]
\textbf{SOFAS dgender 2 OLS CLL} & \textbf{} & \textbf{} & \textbf{} & \textbf{0.500} & \textbf{0.537}\\
\cmidrule{1-6}\pagebreak[0]
SD (Intercept) & 0.481 & 0.209 & 0.031, 0.718 &  & \\
\cmidrule{1-6}\pagebreak[0]
Intercept & -1.087 & 0.065 & -1.215, -0.960 &  & \\
\cmidrule{1-6}\pagebreak[0]
SOFAS scaled & 0.940 & 0.091 & 0.763, 1.118 &  & \\
\cmidrule{1-6}\pagebreak[0]
dgenderMale & 0.224 & 0.029 & 0.167, 0.278 &  & \\
\cmidrule{1-6}\pagebreak[0]
dgenderOther & -0.196 & 0.096 & -0.385, -0.009 &  & \\
\cmidrule{1-6}\pagebreak[0]
dstudyingworkingBoth & 0.159 & 0.041 & 0.078, 0.240 &  & \\
\cmidrule{1-6}\pagebreak[0]
dstudyingworkingStudy & 0.148 & 0.037 & 0.076, 0.218 &  & \\
\cmidrule{1-6}\pagebreak[0]
dstudyingworkingWork & 0.070 & 0.043 & -0.013,  0.156 &  & \\*
\end{longtable}

\newpage

\end{document}
